Data analysis
The ecosystem multifunctionality (EMF) indexes of alpine steppes with and without shrub encroachment were calculated by five plant functions (Cover, Height, SR , AGB, and BGB) and seven soil functions (SW, SOC, MBC, STN, MBN, NO3−N and NH4+−N), which were also reclassified into aboveground ecosystem multifunctionality (AEMF) index and belowground ecosystem multifunctionality (BEMF) index. These indexes were calculated as follows:
\begin{equation} EMF=\frac{1}{N}\sum_{i=1}^{N}\text{Zij}\nonumber \\ \end{equation}
where N represents the total number of functions evaluated andZij is the standardization (Z-score) of the i th ecosystem function in the j th plot.
We further used the relative interaction intensity (RII) to estimate the changes magnitude of the ecosystem functioning in semi-arid alpine steppes induced by shrub encroaching. The RII index was calculated as:
RII=(VSE−V) / (VSE + V)
where VSE and V are the values of ecosystem individual functions in shrub encroached and non-encroached alpine steppes, respectively. The RII values >0 indicating a positive impact shrub encroachment on the individual and multiple ecosystem functioning.
The independent sample t -test was used to test the differences in vegetation characteristics, soil variables and the EMF indexes between alpine steppes with and without shrub encroachment. Two-way analysis of variance (ANOVA) tested the impacts of shrub type and shrub encroachment, and their interactions on the individual and multiple ecosystem functioning. We further used the Pearson correlation to explore the relationships among the individual ecosystem functions as well as the ecosystem multifunctionality indexes.